← etc / Encyclopedia of Triangle Centers

X₃₀₂₉¶

INTERSECTION X₁₀X_115∩X₉₈X_573

X₃₀₂₉ = complement of X₃₈₄₈₁

X₃₀₂₉ (INTERSECTION X₁₀X_115∩X₉₈X_573) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3029 = INTERSECTION X_10X_115∩X_98X_573."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03029(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3029 = INTERSECTION X_10X_115∩X_98X_573 on reference triangle ABC."""
            X_3029 = eval_trilinear_point(model, A, B, C, '(b*c*(b + c)**(2)*(a**(3) + a**(2)*c - a*b**(2) - b**(3))*(a**(3) + a**(2)*b - a*c**(2) - c**(3)))', ID="X_3029", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            central_line(model, X_10, X_115, 10, 115, incident=True)
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            X_386 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2) + b*c + c*a + a*b)', ID="X_386", classes=["center", "incident"])
            central_line(model, X_99, X_386, 99, 386, incident=True)
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            X_573 = eval_trilinear_point(model, A, B, C, 'cos(A + U)', ID="X_573", classes=["center", "incident"])
            central_line(model, X_98, X_573, 98, 573, incident=True)
            return promote_point_to_top(model, X_3029)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_3029 on the given reference triangle."""
            model = create_model('X_3029 = INTERSECTION X_10X_115∩X_98X_573')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03029(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-03029.json"))
            write_center_svg(
                model_acute,
                here / "x-03029.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3029¶

X₃₀₂₉¶